Streaming video locally is actually really easy, thanks to the software we installed earlier. Just log to the Yun again via SSH, and type:
mjpg_streamer -i "input_uvc.so -d /dev/video0 -r 640x480 -f 25" -o "output_http.so -p 8080 -w /www/webcam" &
http://myarduinoyun.local:8080/stream.html
In Wirecast, you need to add a new "Web stream" with the following parameters: HTTP protocol, Motion JPEG format, and "nameofyourYun.local:8080/?action=stream" as the URI. This picture shows the parameters I used: